Can I know the differences between a Stationary Economy and an Evenly Rotating Economy? Mises says in ‘Human Action’ that an ERE economy is a stationary economy, but the stationary economy is not necessarily an ERE economy? Why so?
Does a Stationary economy mean an economy where there is a fixed amount of wealth, and so, one person’s gain is another person’s los (That is a zero sum situation)?
Human Action gives a pretty clear definition of the stationary economy:
The stationary economy is an economy in which the wealth and income of the individuals remain unchanged.
So, yes, I believe your interpretation in the second question is correct. The evenly rotating economy is a fictitious economy in which equilibrium has met. That is, there is a perfect relationship, for example, between supply and demand. The evenly rotating economy ignores the existance of dynamics in the market (as explained by Mises).
The difference between the two is that the stationary economy does not assume that equilibrium has been met, it only assumes that when there is an increase in demand in sector A, then there must be an equivalent decrease in demand in sector B to free up the necessary resources for sector A. More specifically, A must expand at the same rate as B contracts.
For Mises, the evenly rotating economy was a useful fictitious economic tool because it served as a way to understand human action (the relationship between consumers and production).
Jonathan gave a good explanation, and as a little post-script, I’d like to add that, as I understand it, an Evenly Rotating Economy will never actually be seen in the real world, because it requires that participants have full knowledge of future events and that their actions repeat in an endless cycle. Oppositely, the stationary economy is seen in the real world, because it merely requires that an economy not be expanding or contracting, and, so, the stationary economy probably comes into actual being for extremely brief moments of time occasionally (i.e. when a “bust” occurs and an expanding economy turns around into a contracting economy, at the precise point of the turnaround, it is likely that there is a stationary economy for a very brief moment).
EDIT: As a further post-post-script, after thinking about it, I guess a stationary economy comes into existence much more frequently than I thought. Technically, if you could divide up time into parts so small that the segment of time measured only extended between one action that affected the economy and the next action that affected the economy, that tiny tiny fraction of time in between would constitute a stationary economy for a flash. 
I have got it right now. Thanks both of you.